Factoring Polynomials

Slides:

Advertisements

Similar presentations

6.1 Factoring Polynomials

Advertisements

ZEROS=ROOTS=SOLUTIONS Equals x intercepts. Another Memory slide.

Multiplying and Dividing Monomials. Objectives: Understand the concept of a monomial Use properties of exponents to simplify expressions.

Chapter 6 Polynomials.

Simplifying a Variable Expression

Warm-up: Simplify. 1.6 (3x - 5) = 18x (2x + 10) = 8x y - 3y = 6y 4.7a + 4b + 3a - 2b = 10a + 2b 5.4 (3x + 2) + 2 (x + 3) = 14x + 14.

Laws of Exponents: Dividing Monomials Division Rules for Exponents.

Using the Quotient of Powers Property

Chapter 6 Polynomial Functions and Inequalities. 6.1 Properties of Exponents Negative Exponents a -n = –Move the base with the negative exponent to the.

Do Now Find the GCF of each set of numbers. 1)34, 51 2)36, 72 3)21, 42, 56.

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF.

Notes - Solving Quadratic Equations in Factored Form If ab = 0, then a = 0 or b = 0 If the product of two factors is zero, then at least one of the factors.

Chapter 5: Polynomials & Polynomial Functions

To multiply a polynomial by a monomial Multiply the numbers together Multiply the same letters together by adding the exponents Ex – 3x 3 y 6 z 8 ( 5x.

Simplify a rational expression

Properties of Exponents

6.1 Factoring Polynomials Goal: To factor out a common factor of a polynomial.

Evaluating Algebraic Expressions 4-4 Multiplying and Dividing Monomials Math humor: Question: what has variables with whole-number exponents and a bunch.

Algebraic Operations. Goals Add and subtract algebraic expressions and simplify like terms by applying commutative, associative, and distributive properties.

Warm-Up 1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x , if x = 3 2. (f + g)(x) = ____ for g(x) = 3x2+ 2x and f(x) = 3x (f/g)(x)

February 14 th copyright2009merrydavidson. RATIONAL EXPONENTS 1) Anything to a power of zero =. 1 1.

Factoring Polynomials: Part 1

DIVISIBILITY RULES.

Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

Goals: Use the distributive property to factor a polynomial. Solve polynomial equations by factoring. Eligible Content: A

Adding & Subtracting Polynomials (1.2.1) September 11th, 2015.

Factoring Polynomials: Part 1 GREATEST COMMON FACTOR (GCF) is the product of all prime factors that are shared by all terms and the smallest exponent of.

Problems of the Day Simplify each expression. 1. 9m 2 – 8m + 7m 2 2. (10r 2 + 4s 2 ) – (5r 2 + 6s 2 ) 3. (pq + 7p) + (6pq – 10p – 5pq) 4. (17d 2 – 4) –

8 4 Multiply & Divide Rational Expressions

Algebra 1 Mini-Lessons 3x2y(6y + 12xy − 9x) 3(6x2y2 + 12x3y3 − 9x3y)

Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. ANSWER –9, 9 1. The square roots of 81 are ? and ?. 2. In the expression 2 5, the.

Copy down the following expressions and circle the like terms. 1. 7x 2 + 8x -2y + 8 – 6x 2. 3x – 2y + 4x 2 – y 3. 6y + y 2 – 3 + 2y 2 – 4y 3 What are like.

Prerequisite Skills VOCABULARY CHECK Copy and complete the statement. ? Terms that have the same variable part are called 1. like terms ANSWER zero ANSWER.

Warm-up Answers:. Homework Answers: P3 (55-58 all, all, odds, all) /1690.

Define and Use Zero and Negative Exponents February 24, 2014 Pages

6.1 Properties of Exponents Use properties of exponents Use negative and zero as an exponent EQ: What are the general rules involving properties of exponents?

7-1 Integer Exponents 7-2 Powers of 10 and Scientific Notation 7-3 Multiplication Properties of Exponents 7-4 Division Properties of Exponents 7-5 Fractional.

(have students make a chart of 4 x 11

Warm up! Simplify the following 1.Paraphrase the rules for multiplying exponents? 2.What order do the exponents have to be in? 3.x 3 x 7 x x 2 4.3x 3 4x.

AIM: How do we multiply and divide polynomials?

Unit 2: Properties of Exponents Jeopardy

Multiplying with exponents

Objectives The student will be able to:

8.2A Factoring using Distributive Property

8-5 Factoring Using the distributive property

Adding and Subtracting Rational Expressions

5.1 Properties of Exponents

In this lesson we will classify, add and subtract polynomials.

Objectives The student will be able to:

Monomials (Ex: 2x): It divides into everything…

Dividing Polynomials.

Multiply a Polynomial by a Monomial

7.5 Factoring Linear Expression

Factoring GCF and Trinomials.

Factoring Expressions 7.EE.1

6.1 Factoring Polynomials

Multiply polynomials When multiplying powers with the same base, keep the base and add the exponents. x2  x3 = x2+3 = x5 Example 1: Multiplying Monomials.

Divisibility Rules.

Divisibility Rules.

Divisibility Rules.

Factoring Polynomials: GCF

Warm Up Rewrite -6x + 2x3 + 1 – 9x in standard form, then name by degree & number of terms. 2) Multiply (x + 3)(5x – 1) 3) Multiply (x – 1)(4x2 +5x –

Unit 2: Properties of Exponents Jeopardy

Dividing Polynomials.

1.3 – Simplifying Expressions

Objective Factor polynomials by using the greatest common factor.

(B12) Multiplying Polynomials

Factoring Polynomials

Ch 1-2 Order of Operations

Presentation transcript:

Factoring Polynomials factor out a common factor

Factoring (Divide): Find a # and/or variable that is divisible by all #’s in the expression. To divide the variable subtract the exponents

Divisible by… 2 if last digit is an even number. 3 if the sum of the digits is divisible by 3 4 if the number formed by the last two digits is divisible by 4 5 if the number ends in 0 or 5 7 Nike Rule: “just do it” (long division) 9 if the sum of the digits  by 9 10 if the last digit is a zero.

“Factoring Polynomials” the REVERSE of the Distributive Property 5(x + 3) = 5x + 15 “Factoring Polynomials” the REVERSE of the Distributive Property

Ex 1:Factor: 10x + 15 2x + 3 Check your answer!!!!!

Ex 2 Factor: 12x + 4 3x + 1 Check your answer!!!!!

Ex 3 Factor: 18x3 + 12x 3x2 + 2 Check your answer!!!!!

Ex 4 Factor: x2 + 7x x(x + 7)

Ex 5 Factor: a2b + 2ab ab(a + 2)

Ex 6 Factor: 5x5y4 + 20xy3 5 x y3 ( ) x4y + 4 5xy3(x4y + 4)

Ex 7 Factor 16y5 + 20y3 4y3(4y2 + 5)

Ex 8 Factor: x3(9 + 25x4)

Ex 9 Factor: 3m3n(4m2n + 3m + 2n)

Ex 10 Factor: 16x(x5 - 2x4 - 3)

Ex 11 Factor: x2(6x2 - 10x + 3)

Ex 12 Factor: 2a2(2a2b4 – ab2 + 6)